To determine whether you should use $\bar{x}$ (sample mean) or $\mu$ (population mean), let's clarify:

• $\bar{x}$ is used when calculating the mean of a sample.
• $\mu$ is used when calculating the mean of an entire population.

Since this question refers to a sample, we will calculate the sample mean $\bar{x}$.

The formula for the sample mean is:

$\bar{x} = \frac{\text{sum of the sample values}}{\text{number of sample values}}$

Given the sample: 15, 11, 5, 10, 19

1. Sum of the values: $15 + 11 + 5 + 10 + 19 = 60$
2. Number of values in the sample: 5

Now, calculate the sample mean: $\bar{x} = \frac{60}{5} = 12$

Thus, the correct answer is:

• A. $\bar{x} = 12$

Would you like more details on this calculation?

Here are some related questions:

1. What is the difference between sample mean and population mean?
2. How do outliers affect the sample mean?
3. Can you explain how to calculate the median of this sample?
4. How would you calculate the standard deviation for this sample?
5. How does increasing the sample size impact the accuracy of the sample mean?

Tip: Always double-check if the data provided is from a sample or a population to choose the correct mean symbol.